Question

factorise √2x2+5x+3√2 by splitting the middle term​

Answer 1

Aim:

We need to factorise the above quadratic polynomial, $\sqrt{2}x^2+5x+3\sqrt{2}$ using the splitting the middle term method.

Procedure of solving:

• The given quadratic polynomial is of the form $ax^2+bx+c$, where $a=\sqrt{2},b=5,c=3\sqrt{2}$.
• For factorising the given quadratic equation, we need to split the middle term $(b)$ in such a way that the product of $a$ and $c$ is formed by its multiplier and multiplicand whose sum results is $b$.
• After splitting the middle term, we can find the factors of the given quadratic polynomial.

Splitting of middle term:

$a=\sqrt{2} ,c=3\sqrt{2}$

$ac=\sqrt{2}\times3\sqrt{2}$

⇒ $3\times2$

⇒ $6$

$2+3=5$

Since, $b=5$

$b=2+3$

$LHS=RHS$

Solution:

$\sqrt{2}x^2+5x+3\sqrt{2}$

$\sqrt{2}x^2+2x+3x+3\sqrt{2}$

$\sqrt{2}x (x+\sqrt{2})+3(x+\sqrt{2})$

$(\sqrt{2}x+3)(x+\sqrt{2})$

∴ The factors of  $\sqrt{2}x^2+5x+3\sqrt{2}$  are $(\sqrt{2}x+3)$ and $(x+\sqrt{2})$.

Answer 2

√2x2+5x+3√2

√2x2+2x+3x+3√2

√2x(x+√2)+3(x+√2)

(√2x+3)(x+√2)

.

. .The factors of √2x2+5x+3√2are (√2x+3)and(x+√2).